Raazesh Sainudiin: Some distributions on finite rooted binary trees with an emphasis on the transmission process

Abstract

We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other fields. In the process we introduce the notions of split-exchangeability and plane-invariance of a general Markov splitting model in order to readily obtain probabilities over various equivalence classes of trees that arise in statistics, phylogenetics, epidemiology and group theory. I might emphasise the distributions of transmission trees that encode the evolution of the simplest epidemic model over a connected contact network of hosts.